Breedsmic temperaments: Difference between revisions
Wikispaces>genewardsmith **Imported revision 268879194 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 289186299 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt> | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-01-03 01:53:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>289186299</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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EDOs: 15, 16, 31, 171, 202 | EDOs: 15, 16, 31, 171, 202 | ||
Badness: 0.0356 | Badness: 0.0356 | ||
==Tertia== | |||
Commas: 385/384, 1331/1323, 1375/1372 | |||
POTE generator: ~22/21 = 77.173 | |||
Map: [<1 3 2 3 5|, <0 -22 5 -3 -24|] | |||
EDOs: 31, 109, 140, 171e, 311e | |||
Badness: 0.0302 | |||
=Harry= | =Harry= | ||
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</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Breedsmic temperaments</title></head><body><!-- ws:start:WikiTextTocRule:36:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><a href="#Hemififths">Hemififths</a><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | <a href="#Tertiaseptal">Tertiaseptal</a><!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --> | <a href="#Harry">Harry</a><!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --> | <a href="#Quasiorwell">Quasiorwell</a><!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --> | <a href="#Decoid">Decoid</a><!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --> | <a href="#Neominor">Neominor</a><!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --> | ||
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<br /> | <br /> | ||
Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | Breedsmic temperaments are rank two temperaments tempering out the breedsma, |-5 -1 -2 4&gt; = 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.<br /> | ||
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Badness: 0.0356<br /> | Badness: 0.0356<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id=" | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Tertiaseptal-Tertia"></a><!-- ws:end:WikiTextHeadingRule:10 -->Tertia</h2> | ||
Commas: 385/384, 1331/1323, 1375/1372<br /> | |||
<br /> | |||
POTE generator: ~22/21 = 77.173<br /> | |||
<br /> | |||
Map: [&lt;1 3 2 3 5|, &lt;0 -22 5 -3 -24|]<br /> | |||
EDOs: 31, 109, 140, 171e, 311e<br /> | |||
Badness: 0.0302<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:12:&lt;h1&gt; --><h1 id="toc6"><a name="Harry"></a><!-- ws:end:WikiTextHeadingRule:12 -->Harry</h1> | |||
Commas: 2401/2400, 19683/19600<br /> | Commas: 2401/2400, 19683/19600<br /> | ||
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Badness: 0.0341<br /> | Badness: 0.0341<br /> | ||
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Commas: 243/242, 441/440, 4000/3993<br /> | Commas: 243/242, 441/440, 4000/3993<br /> | ||
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Badness: 0.0159<br /> | Badness: 0.0159<br /> | ||
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Commas: 243/242, 351/350, 441/440, 676/675<br /> | Commas: 243/242, 351/350, 441/440, 676/675<br /> | ||
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Badness: 0.0130<br /> | Badness: 0.0130<br /> | ||
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In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.<br /> | ||
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Badness: 0.0358<br /> | Badness: 0.0358<br /> | ||
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Commas: 2401/2400, 3025/3024, 5632/5625<br /> | Commas: 2401/2400, 3025/3024, 5632/5625<br /> | ||
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Badness: 0.0175<br /> | Badness: 0.0175<br /> | ||
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Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095<br /> | Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095<br /> | ||
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Badness: 0.0179<br /> | Badness: 0.0179<br /> | ||
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Commas: 2401/2400, 67108864/66976875<br /> | Commas: 2401/2400, 67108864/66976875<br /> | ||
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Badness: 0.0339<br /> | Badness: 0.0339<br /> | ||
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Commas: 2401/2400, 5832/5825, 9801/9800<br /> | Commas: 2401/2400, 5832/5825, 9801/9800<br /> | ||
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Badness: 0.0187<br /> | Badness: 0.0187<br /> | ||
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Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | Commas: 676/675, 1001/1000, 1716/1715, 4225/4224<br /> | ||
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Badness: 0.0135<br /> | Badness: 0.0135<br /> | ||
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Commas: 2401/2400, 177147/175616<br /> | Commas: 2401/2400, 177147/175616<br /> | ||
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Badness: 0.0882<br /> | Badness: 0.0882<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:32:&lt;h2&gt; --><h2 id="toc16"><a name="Neominor-11-limit"></a><!-- ws:end:WikiTextHeadingRule:32 -->11-limit</h2> | ||
Commas: 243/242, 441/440, 35937/35840<br /> | Commas: 243/242, 441/440, 35937/35840<br /> | ||
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Badness: 0.0280<br /> | Badness: 0.0280<br /> | ||
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<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Neominor-13-limit"></a><!-- ws:end:WikiTextHeadingRule:34 -->13-limit</h2> | ||
Commas: 169/168, 243/242, 364/363, 441/440<br /> | Commas: 169/168, 243/242, 364/363, 441/440<br /> | ||
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